Elementary school classrooms are filled with impressionable young minds learning how to add, multiply, and divide; but few of these students will ever understand the logic and the theory behind their calculations. The works of Plato, Euclid, and Newton, upon which all of modern science and commerce depend, are as much philosophical statements about the structure of the universe as they are mathematical treatises. In “Is God a Mathematician?” Mario Livio attempts to impress upon the reader this fundamental connection between math and philosophy while presenting a “greatest hits” summary of man’s foremost mathematical achievements.

Livio concedes on his first page that the notion of God as a mathematician is “neither a philosophical attempt to define God… nor a shrewd scheme to intimidate math phobics.” Instead, Livio is trying to entice lay readers to crack open his book and appreciate the “omnipresence and omnipotent powers of mathematics.” Its focus is the impressive notion that “the same global, coherent mathematics” can be used by a wide variety of scientists, engineers, economists, and doctors to explain such seemingly divergent topics as factory efficiency and the structure of the universe. Livio attempts to account for these seemingly unrelated applications of math by creating an historical narrative about how mathematicians throughout time have interpreted the “underlying mathematical facility” that appears to govern man’s existence.

Livio’s biggest hurdle to overcome with “Is God a Mathematician?” is making over two millennia of high-level mathematical discoveries accessible to the reader who has never studied the more inscrutable and elaborate non-Euclidean geometry or knot theory. And it would seem that if anyone is primed for success in this difficult endeavor, it’s Livio, who is both an astrophysicist and the head of the Office of Public Outreach at the Hubble Space Telescope Institute. But while his approach is appealing to any curious reader, his inability to draw concrete conclusions is frustrating for even the most forgiving one.

Livio struggles to answer the fundamental question of whether mathematicians have “discovered” the universe’s laws or the laws of mathematics were “invented” by mathematicians. Reaching back to the sixth century B.C., Livio uses Pythagoras, Plato, and Archimedes to demonstrate that there is an intimate relationship between the most basic arithmetic and much more complicated and inaccessible abstract logic. Revelations abound, from the logical basis for counting, to the foundation of prime numbers, and the Pythagorean Theorem. But there are an equal number of instances where Livio’s explanations fall short, such as when he discusses knots or how gravity operates in the solar system. In these cases, Livio loses himself in the history of the discoveries and overwhelms the reader with superfluous information and terminology.

“Is God a Mathematician?” is driven by Livio’s love for math and his personal desire to share his awe at its power to explain worldly phenomena. Despite his passion, both Livio’s writing and argument are uneven. At times his prose reads like a history textbook, at others like a review of the latest research in astrophysics. Belying his vigorous attempt to write to the reader, Livio struggles in vain to include sufficient background information necessary for the average reader to match his own remarkable comprehension and unique enthusiasm.

This gap between Livio and his readers is exacerbated by his failure to reach a satisfying conclusion in the closing pages of “Is God a Mathematician?”. After lauding mathematics as the key to understanding the universe for eight chapters, Livio writes that “mathematics is indeed extraordinarily effective for some descriptions, especially those dealing with fundamental science, but it cannot describe our universe in all its dimensions.” He explains that the predictive and explanatory powers of mathematics have been amplified by scientists who choose to work on problems that they know are “amenable to a mathematical treatment.” While this may be accurate, it is a frustrating and unexpected end that contradicts much of what Livio argues for in the earlier sections of his book.

Readers looking to glean divine revelations about the relationship between mathematics and the universe’s structure will be sorely disappointed by “Is God a Mathematician?” Livio leaves the reader with the ambiguous notion that mathematics is in part developed by the mathematicians who study it and also inherent to the natural world around us, waiting to be discovered by intrepid and persistent minds.

Livio is most successful in communicating a deep respect for the power of mathematics and the intellectually rigorous theory behind it that many will never understand. By opening the door to mathematical theory, “Is God a Mathematician?” casts doubt on the absolute truths of arithmetic and geometry that are taught in school and brings Livio one step closer to making enthusiastic readers appreciate the wonder and sophistication of abstract math.

—Staff Writer Eric M. Sefton can be reached at esefton@fas.harvard.edu.